LONDON — President Obama will meet with Western European leaders on Sunday and Monday amid a growing sense in his administration that Europe is faltering in the face of multiple challenges, undercutting the trans-Atlantic alliance at a critical time.

Even as Mr. Obama has tried to focus United States foreign policy more on Asia and China’s rising power, administration aides say they have watched with concern as European unity has come under increased strain at a time of increased Russian aggression, slow economic growth, a virulent terrorism threat, and a huge influx of migrants from the Middle East and beyond.

In meeting in Germany on Sunday with Chancellor Angela Merkel and on Monday with Ms. Merkel, Prime Minister David Cameron of Britain, President François Hollande of France and Prime Minister Matteo Renzi of Italy, Mr. Obama intends to press his European counterparts on a number of issues, aides said.

They include a new trans-Atlantic trade pact, the need for better intelligence sharing within Europe about the terrorism threat, holding firm against President Vladimir V. Putin of Russia and trying to find a solution to the civil war in Syria.

He is scheduled to give a speech Monday in Germany taking stock of Europe’s challenges.

“This speech allows him to step back at a time when the United States and Europe, together, are dealing with a range of challenges, from counter-ISIL and the threat of terrorism, to the current refugee crisis,” said Benjamin J. Rhodes, the president’s deputy national security adviser.

Mr. Rhodes said part of the president’s address would focus on trade, including efforts by Europe and the United States “to combat the headwinds in the global economy and promote sustainable growth.”

In an interview published in a German newspaper on the eve of his visit there, Mr. Obama said it was “not my place to tell Europe how to manage Europe.” But he said it benefited the United States to have a “strong, united, democratic Europe.” And he said the “serious challenges” facing Europe must be confronted boldly.

“The terrorist attacks in Paris and Brussels were not only strikes on two of the world’s great cities, they were assaults on the values of openness and diversity that we cherish on both sides of the Atlantic,” Mr. Obama said in the German paper, Bild Zeitung. “We’ve learned through painful experience that threats to Europe ultimately become threats to the United States.”

His message was similar in tone to the one he delivered Friday in London, where he bluntly urged British voters to reject a proposal to leave the European Union. He said that Britain was stronger inside the bloc and that a united Europe was in the interests of the United States.

European unity “is under strain,” Mr. Obama said Friday as he stood by Mr. Cameron at a news conference and offered full-throated support for the prime minister’s campaign to keep Britain in the European Union.

At the same news conference, Mr. Obama asserted that “the ties that bind Europe together are ultimately much stronger than the forces that are trying to pull them apart.” But administration aides say they share the fears among European officials in Brussels that a British vote to quit the European Union could pull a vital brick out of an already shaky structure.

“We’ve seen some divisions and difficulties between the southern and the northern parts of Europe,” Mr. Obama said Friday, referring to the euro crisis and migration. “That’s created some strains.”

But there are further tensions between Eastern and Western members of the European Union and NATO, too, over how to manage a more assertive, revanchist Russia, which has torn up the post-Cold War order in Ukraine and is trying to undermine confidence in NATO’s principle of collective defense.

The economy of the European Union has been much slower to recover from the crash in 2008, making the challenge of mass migration from the Middle East and North Africa harder to handle. The confusion and popular fear that matters are not under control have undermined public confidence in Ms. Merkel and in other European leaders, while promoting populism, Islamophobia and ultranationalism among a growing minority of voters.

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President Obama and Prime Minister David Cameron of Britain played golf on Saturday.Credit...Stephen Crowley/The New York Times

Those same forces have also helped to stall negotiations toward a far-reaching trade deal between the United States and the European Union. Opponents, particularly in Germany, argue that the agreement would inevitably favor the interests of large corporations and cause a shift of jobs to outsiders.

Thousands of people protesting the trade deal are expected in Hanover, Germany, on Sunday when Mr. Obama arrives to tour an industrial trade show with Ms. Merkel.

Mr. Obama, whose vision of a stronger, more cohesive Europe includes passage of the trade deal, campaigned Saturday on its behalf in London, where he urged a roomful of young people to view it as a positive approach.

“Part of the argument I’m making in the United States is that the answer to globalization and income inequality and lack of wage growth is not to pull up the drawbridge and shut off trade,” Mr. Obama said.

Among the main concerns of Mr. Obama’s delegation is major, consistent gaps in intelligence gathering and intelligence sharing within Europe when the Islamic State, also known as ISIS or ISIL, is targeting the Continent and exploiting the ease of movement across borders.

That vulnerability prompted Mr. Obama to call together the meeting on Monday with his counterparts from the four biggest Western European nations, to discuss counterterrorism strategies and intelligence sharing.

“They understand how indispensable U.S. intelligence is for understanding who is in the country, where they are moving around,” said Heather Conley, a former State Department official and now a scholar at the Center for Strategic and International Studies. “This is completely weighing down Europe.”

The five leaders are also likely to discuss the situations in Syria and in Libya, where the Islamic State has built a strong presence close to Europe in the chaos that resulted from the Western intervention to overthrow Col. Muammar el-Qaddafi.

The president will be back in Europe for a NATO summit meeting in early July, when many of these same issues will be on the table, including a pronounced political shift to the right in the host country, Poland.

Mr. Obama has already agreed to increase the number of American troops in Europe, announcing in March that he would deploy rotations of United States-based armored brigade combat teams to Eastern Europe to create what officials call a continuous, but not a “permanent,” presence.

But there are also concerns about an increasingly authoritarian presidential regime in Turkey, a NATO member that is a front-line state with Syria. Turkey is also playing an important if controversial role in preventing migrants and asylum seekers from trying to reach Europe by boat.

In the interview in the German paper, Mr. Obama praised Ms. Merkel as being “courageous” in handling of the surge of migrants into Europe from Syria. The president said Ms. Merkel had “spoken of our moral obligation to people, including families and children, fleeing horrific conditions, including the barbarity of the Assad regime in Syria and ISIL.”

The president also used the trip to buck up Mr. Cameron, with whom he played golf on Saturday at the Grove, the site of the 2016 British Masters tournament and one of England’s most luxurious courses.

But the president’s intervention in the British debate over the European Union has been controversial, with a significant number of commentators saying he was overstepping. Robin Niblett, however, the director of Chatham House, a policy institute in London, said the United States was right to try to intervene after having fought two wars in the last century to keep Europe free.

A British exit, Mr. Niblett said, “would potentially destabilize the E.U. at just the wrong time: when a rearmed Russia has rejected the rules-based order created to sustain peace in Europe after the Cold War, when Continental E.U. governments are struggling to manage an unprecedented inflow of refugees and migrants, and when populist parties are gaining in strength on the back of a still painful economic recession for many.”

“And,” he continued, “it would leave just as the U.S. is trying to strengthen the trans-Atlantic relationship in the face of a more economically and politically assertive China.’’